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A population of $ i $ parasites is distributed at random among $ M $ hosts; any host carrying more than $ n $ parasites dies. We first find the expected numbers of hosts carrying $ 0,1, ldots ,n $ par...asites. Parasite-free hosts then produce offspring according to a birth-death process over a breeding season $ T $, while the parasites also breed in a birth-death process, again killing any host carrying more than $ n $ of them at time $ T $. We find the expected number of surviving hosts and the total expected number of surviving parasites after the breeding season. We illustrate the process by a simple example.show more
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